Math Help - Tough linear equations in 2 variable question, can you solve it :)

1. Tough linear equations in 2 variable question, can you solve it :)

SOLVE :-

(3x +2y - 7)^2 +(5x + 7y - 13)^2 = 0, for real values of x and y

well, I'm not bad at maths, it's that this question is too challenging, so please HELP HELP HELP !!!!!

2. Originally Posted by ice_syncer
SOLVE :-

(3x +2y - 7)^2 +(5x + 7y - 13)^2 = 0, for real values of x and y

well, I'm not bad at maths, it's that this question is too challenging, so please HELP HELP HELP !!!!!
Since squares are always greater than or equal to zero, this equation will only have a solution when each of the squares are equal to zero.

So we need to solve the system.

$3x+2y-7=0$

$5x+7y-13=0$

Try either elimination or substition

I got

$x=\frac{23}{11} \mbox{ and }y=\frac{4}{11}$